Portal Financial and Aegon have said there are many issues with the idea floated by Pensions Minister Steve Webb, though Dr Ros Altmann believes it is worth exploring in more depth.
Mr Webb said at the weekend there could be ways to extend the pension freedoms to current annuity holders.
Mr Webb told The Sunday Telegraph retirees would be allowed to sell their annuities at any point to the highest bidder, generating what it described as a new market in second-hand annuities.
The paper reported Mr Webb saying pensioners had urged him to make the change, while some major pensions companies and insurers had also expressed "considerable interest and enthusiasm".
Jamie Smith-Thompson, managing director of Portal Financial, said: "Steve Webb's announcement that he is considering allowing pensioners who have already bought an annuity to sell the product in return for cash is ill-timed and probably ill-conceived."

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He said the reforms already made have caused confusion and he is concerned the latest statement could add to this.
He said: "April isn't very far away now and, as advisers, we are gearing up to answer a host of new questions from people who want absolute clarity around what is, after all, one of the biggest financial decisions of their life. So why choose this moment to throw in yet another radical idea, but this time with no detail or timescale attached?
"It's just going to confuse people even more and may result in some choosing an unsuitable product for their circumstances as they assume more change is definitely around the corner."
Kate Smith, regulatory strategy manager, Aegon UK said: "The industry is already under significant pressure to deliver the various legislative changes this year. The latest proposal from Steve Webb generates a long list of issues and risks for the industry and customers.
"The first and most obvious of these is the fact that a lifetime annuity is priced on the life and medical conditions of that particular customer. So if it were sold on, the new risks and medical conditions would need to be re-priced in as part of the transaction. This might not turn out to be attractive to either the buyer or seller."
Dr Altmann said: "I think this is definitely something worth exploring, but I cannot see it happening immediately. However, it is likely to be a popular idea with many of the five million people who have bought annuities in the past, especially those who feel left out of the new pension freedoms and would prefer to have the benefit of their pension fund rather than a non-inflation-linked and possibly rather small annuity income for life." 

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